Optimal allocation of relevations in coherent systems

In this paper we study the allocation problem of relevations in coherent systems. The optimal allocation strategies are obtained by implementing stochastic comparisons of different policies according to the usual stochastic order and the hazard rate order. As special cases of relevations, the load-sharing and minimal repair policies are further investigated. Sufficient (and necessary) conditions are established for various stochastic orderings. Numerical examples are also presented as illustrations.

Residual Probability Function for Dependent Lifetimes

In this paper, the residual probability function is applied to analyze the survival probability of two used components relative to each other in the case when their lifetimes are dependent. The expression of the function by copulas has been derived along with some examples of particular copulas. The behaviour of the residual probability function in terms of the underlying dependence is also discussed. The residual probability order is also considered in the dependent case. In the class of Archimedean survival copulas, we prove that the residual probability order implies the usual stochastic order in the reversed direction, and the hazard rate order concludes the residual probability order.

ORDERINGS OF FINITE MIXTURE MODELS WITH LOCATION-SCALE DISTRIBUTED COMPONENTS

In this paper, we consider finite mixture models with components having distributions from the location-scale family. We then discuss the usual stochastic order and the reversed hazard rate order of such finite mixture models under some majorization conditions on location, scale and mixing probabilities as model parameters.

Stochastic Comparisons of Parallel and Series Systems with Type II Half Logistic-Resilience Scale Components

This paper deals with stochastic comparisons of two parallel (series) systems with Type II half logistic-resilience scale (TIIHL-RS) distribution components with different baseline distribution functions. Under the conditions of interdependency and independency, the research shows that the system performance is better (worse) with the stronger component heterogeneity in the parallel (series) system under the usual stochastic order and the (reversed) hazard rate order.

ORDERING RESULTS ON EXTREMES OF EXPONENTIATED LOCATION-SCALE MODELS

In this paper, we consider exponentiated location-scale model and obtain several ordering results between extreme order statistics in various senses. Under majorization type partial order-based conditions, the comparisons are established according to the usual stochastic order, hazard rate order and reversed hazard rate order. Multiple-outlier models are considered. When the number of components are equal, the results are obtained based on the ageing faster order in terms of the hazard rate and likelihood ratio orders. For unequal number of components, we develop comparisons according to the usual stochastic order, hazard rate order, and likelihood ratio order. Numerical examples are considered to illustrate the results.

Preservation of the mean residual life order for coherent and mixed systems

The signature of a coherent system has been studied extensively in the recent literature. Signatures are particularly useful in the comparison of coherent or mixed systems under a variety of stochastic orderings. Also, certain signature-based closure and preservation theorems have been established. For example, it is now well known that certain stochastic orderings are preserved from signatures to system lifetimes when components have independent and identical distributions. This applies to the likelihood ratio order, the hazard rate order, and the stochastic order. The point of departure of the present paper is the question of whether or not a similar preservation result will hold for the mean residual life order. A counterexample is provided which shows that the answer is negative. Classes of distributions for the component lifetimes for which the latter implication holds are then derived. Connections to the theory of order statistics are also considered.

ON THE OPTIMALITY OF A STRAIGHT DEDUCTIBLE UNDER BELIEF HETEROGENEITY

This article attempts to extend Arrow’s theorem of the deductible to the case of belief heterogeneity, which allows the insured and the insurer to have different beliefs about the distribution of the underlying loss. Like Huberman et al. [(1983) Bell Journal of Economics14(2), 415–426], we preclude ex post moral hazard by asking both parties in the insurance contract to pay more for a larger realization of the loss. It is shown that, ceteris paribus, full insurance above a constant deductible is always optimal for any chosen utility function of a risk-averse insured if and only if the insurer appears more optimistic about the conditional loss given non-zero loss than the insured in the sense of monotone hazard rate order. We derive the optimal deductible level explicitly and then examine how it is affected by the changes of the insured’s risk aversion, the insurance price and the degree of belief heterogeneity.

Hazard rate ordering of the largest order statistics from geometric random variables

Mao and Hu (2010) left an open problem about the hazard rate order between the largest order statistics from two samples of n geometric random variables. Du et al. (2012) solved this open problem when n = 2, and Wang (2015) solved for 2 ≤ n ≤ 9. In this paper we completely solve this problem for any value of n.

COMPARISONS OF SAMPLE RANGES ARISING FROM MULTIPLE-OUTLIER MODELS: IN MEMORY OF MOSHE SHAKED

In this paper, we discuss the ordering properties of sample ranges arising from multiple-outlier exponential and proportional hazard rate (PHR) models. The purpose of this paper is twofold. First, sufficient conditions on the parameter vectors are provided for the reversed hazard rate order and the usual stochastic order between the sample ranges arising from multiple-outlier exponential models with common sample size. Next, stochastic comparisons are separately carried out for sample ranges arising from multiple-outlier exponential and PHR models with different sample sizes as well as different hazard rates. Some numerical examples are also presented to illustrate the results established here.